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DELIVERED AT THE 



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GENEVA COLLEGE, 



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AUGUST 4, 1841. 



BY BENJAMIN HALE, D. D., 

PKESIDENT. 



PUBLISHED BY REQUEST OF THE TRUSTEES 




GENEVA, N. Y.: 

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I8T2. 



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On the occasion of delivering my first Baccalau- 
reate Address, three years ago, I commenced what 
I designed should be a series of discourses on Edu- 
cation, "in its relation to the full and free develope- 
ment of the reason and the understanding," intend- 
ing to exhibit therein an extended view of the true 
scope and means of a liberal education, as demanded 
by a community in the full enjoyment of free insti- 
tutions. 

It is the common faith among us, that our free 
institutions rest ultimately on the knowledge and vir- 
tue of the people ; but, in interpreting this common 
faith, the right of private judgment is most freely 
exercised. Every one regards himself as at liberty, 
and few are so modest as not to believe themselves 
fully competent, to define the knowledge, which is 
necessary to the citizen of a free state. And what 
is the consequence I That which each understands, 
the bearing of which he can see, he sets down as 
necessary ; that on the other hand, which lies beyond 
his scope, or which appears to him to be conducive 
to the distinctioa- of its possessor, while its impor- 
tance to the whole community, however great, he 
does not understand, he regards as a matter in which 



the public has no concern. Narrow views are be- 
gotten, and the value of learning in itself is inade- 
quately estimated. Learning declines, and it is found 
too late, that common education, and the general 
intelligence of the people decline with it. Such 
seems to be, in brief, the course to which things are 
tending, upon this most important subject, in our 
country. The high estimate of learning for its own 
sake, and from enlarged views of the benefits of the 
highest provision for the nourishment of the intel- 
lect, which was once prevalent in some of the older 
parts of our land, seems to exist no longer in the 
same power and purity; and too generally that 
only is valued, the immediate application of which to 
the business of living, is apparent to the unlearned 
and unreflecting. There is among us a strong 
tendency to belieiie only what we can see. Men 
see not, and it is impossible that they should see 
the full value of the learning which they do not 
possess, and they cast it out of their creed. So 
far, however, as they see, they believe, and hence 
while comparatively little wisely directed effort has 
been made for the promotion of university education, 
it has become popular to expend vast sums for the 
support of common schools. 

Against such expenditure, I have nothing to ob- 
ject. There is no kind of internal improvement so 
important, or which will yield so large a revenue, as 
the improvement of the mind and heart of the peo- 
ple. I would only, that men should so value the 
streams and rivulets which carry fertihty to every 



door, as not to look upon the ocean, from whose 
bosom their waters have been drawn up in vapor, 
as a useless waste. I w ould, that they should have 
faith in something which they do not see, — if not in 
the opinions of those who are best qualified to judge 
in such matters, yet in the immortal and rational 
nature of man, as his highest glory, and the origin 
of all, that in human character and society is most 
excellent. Then would they believe, that in the high- 
est cultivation of the reason is to be found the means 
of carrying to higher and still higher elevation, his 
superiority. The soul of man is a mystery, and it 
might well be admitted that its nourishment, and its 
action even in things which most concern men, should 
have something in them which the w holly unlearned 
should not be able to expound. Had men such a 
measure of faith, is there any thing capable of being 
known which would be ridiculed as a subject of 
human enquiry] — anything too abstract, anything 
too recondite, any thing too apparently remote from 
human concerns to deserve attention 1 We know 
well, that we are sometimes compelled to go into 
abstractions J to find the principles on which the most 
important practical questions are to be settled, espe- 
cially w^hen these questions are out of the common 
course of events, and precedents and analogies fail 
us ; and the profounder the abstractions, if we reach 
them by accurate analysis, and reason from them 
exactly, the more valuable our deductions. We 
know too, that the recondite is not therefore useless. 
All that is true and good does not lie upon the sur- 



face. The richest treasures of the earth are deeply 
hidden within its bowels, and many of the great prin- 
ciples of physical science, w hich are so full of prac- 
tical applications to the uses of life, have but re- 
cently been brought to light, after a search of many 
generations. So, too, the 7 emote can never be too 
far removed to concern us, and to concern us nearly. 
The remote sun warms us, and the remote stars are 
our silent time-keepers. Nay, these distant orbs are 
the very guides of the sailor upon the trackless ocean, 
and he then only feels lost in his desert w ay, when 
" neither sun nor stars in many days appear." I 
suppose that the Danish astronomer, as he watched 
the stars from his island observatory, and, year after 
year, studied the distant heavens, may have been the 
standing jest of many a rude navigator of the Baltic, 
who little dreamed how great practical results, touch- 
ing the comfort and the safety of none more closely 
than of the sailor, w ere to come of this, as he thought 
it, idle star-gazing. Let human thought expand itself 
where it w ill, its earnest application can scarcely be 
without fruit. Let learning of any kind be pursued 
in a serious way, it cannot be without profit, and 
may lead to benefits, no one can say how great, or 
how widely diffused. Let it not be left, then, to men 
of unexpanded minds to decide what kind or extent 
of learning shall be thought worthy of public sup- 
port ; nor let it be supposed that what is expended 
for the education of a learned class, is lost to the 
community. If it come not back in some grand dis- 
covery, which blesses and enriches an age, it is certain 



to return, with interest, in the weekly instructions of 
the pulpit, in the labors of well-taught teachers, of 
thoroughly educated physicians, or lawyers or legis- 
lators. And let me add one remark more to this 
point. Let it not be thought that University Educa- 
tion, if supported at the public expense, ought there- 
fore to adapt itself to the popular taste, or popular 
notions of what is fitting, without farther question, 
or any serious and strenuous effort to give the popu- 
lar taste and popular notions a right direction. Let 
" learning made easy" be left to those who can nei- 
ther attain nor impart it in any higher shape, — but 
let our highest institutions be not only suffered, but 
sustained in their high duty of imparting mature learn- 
ing in a manly way, and of making scholars, whose 
well-disciplined minds and sound learning shall be 
ready for any of the higher services of the republic. 
The value of such a service can certainly be made 
apparent to an intelhgent people, and will be appre- 
ciated. 

In my last address upon a similar occasion,* I con- 
sidered the study of the Latin and Greek Languages 
as a part of liberal education, and I trust, sufficiently 
vindicated their claim to the place they have so long 
held, and the careful study of them as among the best 
means of intellectual discipline, and as performing 
a part in this important process, for which nothing 
else yet devised can be successfully substituted. 

In my present discourse, I shall say a few words 

* In 1839. The usual Address at the Commencement of 1840, was omitted 
on account of the imperfect health of the author. 



8 

on the study of Mathematics. The Languages, and 
the Mathematics, are properly regarded as the two 
fundamental parts of education. The discipline 
which they severally gave, is as different as that of 
any two studies can well be, while they seem to 
cover the whole ground of the elementary train- 
ing of the understanding. The one exhibits nfioral 
reasoning — the other, demonstration in its sim- 
plest form. I shall not be obliged on this subject, 
as on the former, to undertake a defence against 
popular prejudice and misjudgment. The use of 
Mathematical learning is too manifest, and exhib- 
its itself too clearly in the business and improve- 
ment of modern times to permit it to be over- 
looked. We keep and settle our accounts — we 
measure our land — we lay out our rail-roads and 
canals — we establish our weights and measures — 
we obtain our time — we find our place on the 
earth's surface, or our path upon the ocean, by the 
means of this science. Not that pure Mathematics 
contains all that is necessary for all these purposes, 
but it constitutes the language and the logic by 
which all reasoning upon number and quantity 
must be conducted. The language of moral sub- 
jects, that in which reasoning of the probable 
kind is conducted, is the ordinary language of men, 
the language which we begin to speak at our first 
lisping. We overlook its scientific dignity in its 
commonness, and, regarding it merely as a means of 
communication, not as an instrument of reasoning, 
we seem to ourselves to learn it sufiiciently by use, 



without making it an object of distinct and care- 
ful study. Not so with the language of number 
and quantity. It is learned at a maturer age, and 
under the impression of its scientific character. It 
is learned by all in its more elementary forms, be- 
cause the affairs of civilized life cannot be con- 
ducted without it ; and those who apply themselves 
to the attainment of a liberal education, are en- 
couraged to pursue it into its highest forms of rea- 
soning, and its profoundest abstractions, because it 
is perceived that more knowledge of it than is re- 
quired for the ordinary business of life, is necessary 
for the settlement of questions, and the conducting 
of affairs, which are of the highest moment to the 
peace and advancement of society. 

In the early days of our country, the study of the 
learned languages and of logic, constituted by far 
the most important part of university education. 
At that period the subjects which most interested 
and agitated men, were moral and political. Reli- 
gion was regarded as the highest object of learning ; 
and the sacred records of Christianity were written 
in one of the learned languages of antiquity, and the 
works of theologians principally in the other. In- 
deed, the language of the learned was the Latin, and 
those who wrote for Europe, rather than the partic- 
ular country in which they lived, wrote in the lan- 
guage of Cicero and the Caesars. The study of the 
languages and of logic, therefore, was demanded by 
the circumstances of the age, and suited its general 
current of thought and of speculation. At the pre- 



10 

sent day, we are not so much occupied with high and 
abstract questions of moral and rehgious, and I must 
be pardoned if I add pohtical rights and obligations, 
as with the outward machinery of living comfortably, 
and carrying forward the material progress of so- 
ciety. Railroads and canals, the settlement of 
boundaries, and the exact survey of our new terri- 
tory, and the marking it by lines which can be found 
again by the stars, should all terrestrial metes and 
boundaries be destroyed, are among the great ques- 
tions of the present day. Even politics deals more 
with mathematical than with moral reasoning, and 
takes the shape of Statistics or Economics, or of 
calculation in the less dignified form of the proba- 
bilities of elections ; and Religion itself, if I mistake 
not, has not escaped the influence of this " spirit of 
the age," though upon this topic I would here sim- 
ply suggest the enquiry, whether the profound and 
earnest search for the right has not been too much 
forgotten in the eagerness for the expedient, and 
calculation too much taken the place of an humble 
and reverent love of truth. Such a change in the 
character, objects and tendencies of the age, could 
not but show itself in our universities, and in the 
increased popularity of the physical sciences, and 
the sciences of calculation. It is a change from the 
moral to the mechanical, from a devotion to abstract 
truth in religion and politics, to a devotion to the 
outward improvement of our fortunes, and the de- 
velopement of the resources of our country. It has 
brought with it a change in the general current of 



11 

thought, and the necessity of a kind of learning, 
before Httle cultivated. 

This great change I do not speak of by way of 
censure ; it has taken place in the course of events, 
leading us on as a people to the fulfilment of our 
destinies. The former epoch naturally terminated 
with the war of the Revolution, when those great 
principles of civil liberty, which had been working 
in men's minds and formed the end and scope of so 
much of their study and meditation, were secured 
by the securing of our national independence, and 
by the same event we were put in possession of a 
country, to be governed by ourselves without re- 
straint — a country of vast resources, unknown but 
continually unfolding themselves to stimulate the 
energies of an enterprising people. The moral had 
had its result — the mechanical was to follow. The 
moral peopled the country originally, and estab- 
lished it as the home of liberty and a refuge for the 
oppressed of other lands, — the mechanical estab- 
lishes commerce and manufactures, constructs rail- 
roads and canals, and works out all the other visible 
means of national wealth. 

It is remarked by Mr. De Tocqueville, "that the 
" spirit of the Americans is averse to general ideas ; 
" and that it does not seek theoretical discoveries."* 
This remark applies to the present state of things 
in our country, and finds its explanation in the cause 
which I have just pointed out. That it is not ap- 
plicable to the earlier portion of our history, we 

* Democracy, vol. i, p. 296. 



12 

need no other authority to assure us than the 
same able writer. "In studying the laws," says he, 
" which were promulgated in the first era of the 
"American republics, it is impossible not to be 
" struck by the remarkable acquaintance with the 
"science of government and the advanced theory 
" of legislation which they display. The ideas there 
" formed of the duties of society towards its mem- 
" bers, are evidently much loftier and more compre- 
" hensive than those of European legislators at that 
" time.^" " The boldest theories of human reason 
" were put in practice by a community so humble, 
" that not a statesman condescended to attend to it."t 

Such a change as I have spoken of then has taken 
place. Within its just limits, it was important and 
necessary. Whether these limits have been trans- 
cended — whether in pushing forward the mechan- 
ical improvements of our age, we have not lost in 
too great a degree, the spirit of the former epoch, 
and whether this may not be precisely the ground of 
the greatest existing dangers to American liberty, 
let the reflecting decide. I am led to speak of it, in 
consequence of its influence on our systems of in- 
struction, producing a change in all ; but more deci- 
dedly apparent in those newer parts of our country, 
which are less influenced by the often salutary, but 
not often commended force of prescription, and 
venerable custom. 

Without the apparatus of our universities and 
schools, and just the direction of studies which for- 

* Democracy, vol. i, p. 23. f lb., p. 24. 



13 

merly existed, the past generation would not have 
been prepared to fulfil the part assigned it ; nor with- 
out the existence of means in much higher degree 
than they were enjoyed among us before the Revolu- 
tion, to train a competent number of young men in 
the mathematical sciences, would the present have 
been able to discharge its duties. The change on 
this point however, has in general been much too 
sweeping. 

It will easily be remembered by those who were 
educated at any of our Colleges twenty or thirty 
years ago, how meagre was the course of mathe- 
matical study, though even then the translation of 
La Place existed in the manuscripts of the self-edu- 
cated Bowditch. Geometry was studied, and in the 
application of Mathematics to the physical sciences, 
the geometrical method of proof alone was used. 
Analysis was almost unknown, except in some mea- 
gre treatises of Algebra, in which the science was 
taught synthetically. This form of Mathematics, 
although well fitted for the purpose of intellectual 
discipline, was but an imperfect instrument of re- 
search, and so long as it prevailed, improvement in 
all the sciences, involving mathematical reasoning, 
could not but be slow. 

For the introduction of the analytical Mathemat- 
ics into the universities and schools of this country, 
we are indebted principally to the Military Academy 
at West Point ; and if this valuable institution had 
rendered no other service to the country than this, 
it would have amply repaid its cost. Consider the 



14 

position of our country after the war of the Revo- 
lution, rich almost beyond example in the capabili- 
ties of wealth and power — possessed by a people 
sprung from the industrious and substantial classes 
of the most enlightened nation of Europe — already 
known for wisdom in council and courage in action, 
and ambitious of an honorable rank among the na- 
tions of the earth ; and how necessary to the devel- 
opement of these capacities, and to these proud 
hopes, and the wonderful changes by which they have 
since been vindicated, was the possession of mathe- 
matical and physical science in its highest form, 
and it will appear how large a debt we owe to this 
institution. There were engineers among us before 
West-Point furnished them, but they were few, and 
the greatly increased resources of civil engineering 
in our country, the perfection and cheapness with 
which important works are executed, and the wide 
diffusion of the knowledge of this important science, 
and that knowledge in a scientific form, are mainly 
attributable to that school. My purpose does not 
lead me to speak of it in other respects, but as a 
source of mathematical knowledge in our country, 
it seemed due from me, led to it as I am by my pre- 
sent subject, to speak of it with the highest acknow- 
ledgments. 

The practical value of the study of Mathematics, 
and its importance in relation to public improve- 
ments and the progress of the arts, are important 
considerations in vindicating its claim to a place in 
a system of liberal education. These considerations 



15 

merely however do not separate it from other 
studies, which are strictly professional, and could we 
urge no more than this, Mathematics might, like the 
law, be regarded as a professional study of the high- 
est importance to be pursued by surveyors, naviga- 
tors and engineers, but not entitled to demand of the 
general student a very careful study of its higher 
mysteries. Its claim to the important place, which 
it holds in a system of liberal education, is grounded 
on its peculiar fitness as a means of intellectual dis- 
cipline, and its necessity, in connexion with other 
means, for the full developement of the powers of 
the understanding in their just proportions. 

The study of Language is important as a means 
of disciplining the mind to moral reasoning, and fur- 
nishes examples of it in the shape most convenient, 
as it seems to me, for elementary instruction. The 
province of demonstration is occupied in a great 
measure by Mathematics, and it is unquestionably 
in this science that we find its simplest forms, and 
the means of training the mind most successfully to 
the exactness of demonstrative reasoning. Although 
a taste for mathematical reasoning may create a de- 
mand for it in cases, in which it is impracticable, and 
beget a sceptical dissatisfaction, in unbalanced 
minds, with other reasoning ; yet by exhibiting in the 
clearest manner and under the simplest forms, the 
true nature of demonstration, the study of this sci- 
ence may lead to the detection of the obstacles, 
which stand in the way of its extension to other prov- 
inces of human knowledge, and thus to their removal. 



16 

The very circumstances, which render Mathemat- 
ics capable of demonstrative reasoning, render it 
the best means of elementary instruction in reason- 
ing vs^ith absolute precision. Its subjects are all 
capable of being precisely stated, and its language 
is free from ambiguity. The slightest error in its 
processes is as palpable as the largest, and an ap- 
proximate result can never be mistaken for an abso- 
lute one. It is concerned wdth the simplest and 
most precise relations, and therefore is suited to 
elementary discipline in exact 'thinking. I do not 
in these remarks intend to imply that our w^hole 
discipline in reasoning can be entrusted to Mathe- 
matics. My conviction is far otherwise. Discipline 
in moral reasoning can be successfully conducted 
only by practice in moral reasoning. Mathematical 
studies may however, most successfully teach the 
young mind what exact reasoning is. An eminent 
jurist once said to me, "Before I studied Geom- 
etry, I never saw light ;" and it is said of another, 
that it was his habit, while holding his courts, to 
read over one or two of Euclid's demonstrations 
every morning. 

The difficulties of mathematical reasoninof, do not 
consist in the obscurity of the separate steps, but 
chiefly in their great number, and the brevity with 
which they are stated. A single theorem may con- 
tain more distinct steps, than a whole vokime of 
argumentation on politics or morals. The brief lan- 
guage of Mathematics expresses in a single symbol, 
what would require a page of ordinary language, 



17 

and its absolute precision renders long explanation 
unnecessary. A dull mind, which cannot master 
or distinctly retain the definitions and fundamental 
processes of mathematical reasoning, and the impa- 
tient one, which hurries over the thronging steps of a 
demonstration without clearly seeing their sequence, 
will find the difficulties of this science oppressive. 
There are few however so dull as not to be able, 
with proper pains at the outset, to attain a distinct 
apprehension of the elementary principles of math- 
ematics, and those who find difficulties in its study, 
from either their dullness or their impatience, may 
derive from it the most valuable discipline. No 
study will more clearly teach the necessity of precise 
and steady views of the elements of a science, in 
order to its successful prosecution, or the general 
truth that step by step is not only the surest, but the 
readiest way to exact conclusions. 

Such, then, is the great value of the Mathe- 
matics as an elementary part of a liberal educa- 
tion. It is a discipline of exactness, of circum- 
spectness, and of patience in the conduct of the 
understanding. It gives positive knowledge which 
no well educated man can be without, and imparts 
to the mind a new instrument of research. 

In considering the importance of Mathematics as 
a part of a liberal course of study, it would be im- 
proper not to notice its bearing upon the progress 
of general philosophy. In a former discourse, I 
spoke of language as the great instrument of anal- 
ysis, and in illustrating its analytical character, re- 



18 

ferred to Algebra, the language of which is the lan- 
guage of analysis in its most perfect form. " The 
principal cause," says Dugald Stewart, "of the over- 
" throw of the sect of the Nominalists, I am disposed 
" to think, was their want of some palpable exam- 
" pie, by means of which they might illustrate their 
" doctrine. It is by the use which algebraists make 
" of the letters of the alphabet in carrying on their 
" operations, that Leibnitz and Berkley have been 
" most successful in explaining the use of language 
" as an instrument of thought."^ 

In meditating upon this subject, it has seemed to 
me that all elementary study resolves itself into the 
study of language, or of the several instruments of 
analysis. Language is the immediate object of 
Logic, v^hich, as Abp. Whately states it, is merely 
" the art of employing language properly for the 
purpose of reasoning." It would be unsuitable to 
the occasion to pursue farther so abstract a subject, 
but if the remark be well founded, that the study of 
Mathematics is the study of one of the great instru- 
ments of analysis, and that the study of these instru- 
ments of analysis, as the means by which the mind 
must pursue its labors in investigation, and in the 
attainment of knowledge, is the most substantial 
ground-workof a thorough education ; it furnishes an 
irrefragable defence of the study of Mathematics, 
and deserves to be profoundly considered by all to 
whom education is entrusted. 

If such then as I have represented are the reasons 

• Phil, of the Hiunan Mind. vol. i. 164. 



19 



for the study of Mathematics in a course of liberal 
education, it is apparent that this study ought to be 
pursued in a manner at once the most exact and 
thoroughly analytical. If the pupil is to learn from 
it the nature of demonstration, and to habituate 
himself to exact reasoning, if he is to avail himself, 
in any measure, of its means for investigating the 
processes of the understanding, and detecting the 
helps which it employs, he must study it with the 
utmost exactness. 

It will be perceived upon the mere mention, that 
in the nature of the training given to the mind, 
Geometry or synthetical Mathematics, differs in 
some respects materially from analysis. In Ge- 
ometry, the proposition is first stated, the point 
to be proved must be kept steadily in view during 
the whole process of the demonstration, and the 
mind receives little aid except from the figure before 
the eye. It is thought by many to be superior even 
to analysis as a means of intellectual discipline. To 
train the mind, as in Geometrical reasoning to pro- 
pose to itself distinctly that which is to be proved, 
and to keep it unwaveringly in view during the pro- 
cess of the argument, is indeed a most important 
part of education ; but whatever advantage we may 
allow it in this respect. Geometry cannot carry the 
mind into these profound generalizations, which are 
perfectly easy by analysis, nor does it so reveal to 
it the aid, which it may derive from a w^ell contrived 
language, or so train it to research ^ 

The extent to which mathematical studies should 



20 

be pursued in a course of liberal education, will be 
differently estimated. Some would give them a pre- 
ponderance, others confine them within narrow lim- 
its. It should be the aim of such a course to devel- 
ope the powers of the mind in harmony, and to cul- 
tivate the habit of forming distinct conceptions, and 
reasoning accurately, not only upon mathematical 
and material subjects, but upon moral, on which 
exact reasoning is at once more difficult, and more 
important, inasmuch as "probability," to use the lan- 
guage of Bp. Butler, " is the very guide of life." An 
exclusively mathematical education then, notwith- 
standing the very important office we have assigned 
to Mathematics, as apart of a hberal course of study, 
would be a very defective one. I make this remark 
to meet an opinion, unfortunately too prevalent, 
which confounds practical with technical education, 
and assumes it as the business of education to teach 
the doing of some particular thing, rather than to 
evolve from the germ in which it is enfolded, the 
rational nature of man, in the fulness and perfect 
harmony of its proportions. 

But while some look upon Mathematics too ex- 
clusively as the source of intellectual discipline, 
and as the great object of practical knowledge ; 
others object to the study of it to any consider- 
able extent, as tending to produce rigidity, and a 
technical habit of mind. The exclusive study of 
Mathematics tends undoubtedly to such results, 
especially in minds of small capacity. But it is 
not peculiar to Mathematics to induce a rigidness 



21 

in intellectual habits. Any study remote from the 
common pursuits of men, and requiring severity of 
application and great exactness will, if devoured 
vv^ith more appetite than digestion, produce a simi- 
lar heaviness. To have one's intellect overborne 
— to be perpetually struggling with subjects too 
weighty for its power, is certainly not the way to 
cultivate vivacity of mind. If one of little strength 
desires to handle his thoughts with the show of ease 
and expertness, he must be cautious [that they be 
not too heavy for his handling. Let him deal with 
lighter studies — let him exercise himself with the 
' graces,' but avoid the discus. If however he would 
attain a manly vigor, he must discipline his intel- 
lect with manly exercises, and as he becomes fa- 
miliar with them and his strength increases, he may 
acquire, if not flippancy, a manly ease and freedom. 
That mathematical studies do not necessarily pro- 
duce rigidity of mind, may be seen by the fact, that 
the most lively people of Europe have cultivated 
them most successfully, and few men, whom it has 
been my happiness to know, have surpassed in viva- 
city the most distinguished of American mathema- 
ticians, the translator and commentator of the Me- 
canique Celeste. One who saw Bowditch in his 
hours of business or recreation, would scarcely sus- 
pect that his mornings were spent in the abstrusest 
mathematical investigations ; and nothing shows 
more clearly the energy of his intellect, than that 
under such labors he should have uniformly retained 
the freshness and vivacity of manner and conversa- 



22 

tion, which always distinguished him. Labors which 
would have crushed another, were his recreation, 
and while devoting the regular hours of business with 
the greatest punctuality and energy to the duties of 
a highly responsible office, he accomplished in his 
hours of leisure a work, which gives him undeniably 
the first place among the men of science of this con- 
tinent. He was at once one of the most profound 
analysts, and one of the most delightful of compan- 
ions — remarkable for the symmetry and simplicity 
of his character, and as free from ever}^ thing false 
or indirect, as the most perfect calculation of his 
favorite science. 

But it is not my purpose to pronounce his eulogy, 
though in an academical discourse on mathematical 
science, the first of American mathematicians might 
fairly claim notice, especially one whose character 
was a beautiful commendation of his pursuits, and 
whose history, an exemplification of the success of 
ability and merit, without adventitious advantages. 

But it is time, young geMtlemen of the graduating 
class, that I address a few words more particularly 
to you. T have been speaking of the value of one 
of the studies, to which your attention has been di- 
rected, since you have resided among us, and in 
which you have been faithfully trained. I trust you 
do not leave us, without having reaped a good mea- 
sure of the advantages which flow from it, and that 
you will carry with you into the world the habits of 
exact thinking and careful study, in which it has 



23 

been our effort to train you. If you have formed 
such habits, preserve them — confirm them by con- 
stant exercise, and let me assure you that the longer 
you live, the more highly will you value them. Your 
highest duties in life, and your highest hopes, whe- 
ther of the present or the future, require of you not 
so much brilliancy and ingenuity, as pertinent and 
well-digested knowledge, and soundness of judg- 
ment. Seek earnestly, young gentlemen, to attain 
and to sustain " whatsoever things," in the beau- 
tiful enumeration of the Apostle, " are true, whatso- 
ever things are just, whatsoever things are lovely, 
and of good report." You leave our care, young gen- 
tlemen, but you carry with you our warmest wishes, 
and our prayers, that the blessing of Almighty God 
may be with you, both now and ever. 



LIBRARY OF C2,2lM 



028 316 098 8 



